Question

A block of mass 2kg is pushed against a rough vertical wall with a force of 40N, coefficient of static friction being 0.5. Another force of 15N, is applied on the block in a direction parallel to the wall. If the block will move, then its direction would be
A.)${15^0}$with 15N force
B.)${53^0}$ with 15N force
C.)${45^0}$ with 15N force
D.)${75^0}$ with 15N force

Answer 1

Hint- This question is based on the friction force concept, a resisting force that resists or opposes the motion and acts in the opposite direction of motion for a moving body.

Complete step-by-step answer:
For solving this question we will use the formula of friction force
$F = \mu N$
Where
$\mu$ is the coefficient of friction
N-is the net normal force acting on the object perpendicular to the surface of motion of the object.

Now since the downward force on the block is 20N
And horizontal force is 15N
Resultant force will be

$${F_r} = \sqrt {{{15}^2} + {{20}^2}} \\\ {F_r} = 25N \\\$$

Normal contact force by the wall is 40N
Therefore the friction force will be

$F = \mu N$
$F = 0.5 \times 40 \\\ F = 20N \\\$

The direction of the block is given by
Finding the angle between the resultant force and the frictional force
${\sin ^{ - 1}}\left( {\dfrac{{20}}{{25}}} \right) = {53^0}$
Hence, the correct option is B.

Additional Information:
1. Static friction force- This type of friction force acts on a body kept at rest in the opposite direction of some other force acting on the object.
2. Kinetic force -when the body starts moving then this force opposes the motion of the object . its value is a little bit less than the static friction force.

Note- Generally friction force acts as barrier or opposing in motion of anything like machines, vehicles etc. and causes a lot of losses and tear and fear of friction but it is also very important in some cases like it is the force which enables us to walk on road. The angle of repose lies between 0 and 90 degree.